Springer Series in Light Scattering: Volume 1: Multiple Light Scattering, Radiative Transfer

369 Pages·2018·11.83 MB·English

by  Alexander Kokhanovsky (eds.)

Springer Series in Light Scattering
Alexander Kokhanovsky
Editor
Springer
Series in Light
Scattering
Volume 1: Multiple Light Scattering,
Radiative Transfer and Remote Sensing
Springer Series in Light Scattering
Series editor
Alexander Kokhanovsky, Vitrociset Belgium, Darmstadt, Germany
Editorial Advisory Board
Thomas Henning, Max Planck Institute for Astronomy, Heidelberg, Germany
George Kattawar, Texas A&M University, College Station, USA
Oleg Kopelevich, Shirshov Institute of Oceanology, Moscow, Russia
Kuo-Nan Liou, University of California, Los Angeles, USA
Michael Mishchenko, NASA Goddard Institute for Space Studies, New York, USA
Lev Perelman, Harvard University, Cambridge, USA
Knut Stamnes, Stevens Institute of Technology, Hoboken, USA
Graeme Stephens, Jet Propulsion Laboratory, Los Angeles, USA
Bart van Tiggelen, J. Fourier University, Grenoble, France
Claudio Tomasi, Institute of Atmospheric Sciences and Climate, Bologna, Italy
The main purpose of new SPRINGER Series in Light Scattering is to present
recent advances and progress in light scattering media optics. The topic is very
broad and incorporates such diverse areas as atmospheric optics, ocean optics,
optics of close-packed media, radiative transfer, light scattering, absorption, and
scattering by single scatterers and also by systems of particles, biomedical optics,
optical properties of cosmic dust, remote sensing of atmosphere and ocean, etc.
The topic is of importance for material science, environmental science, climate
change, and also for optical engineering. Although main developments in the
solutions of radiative transfer and light scattering problems have been achieved in
the 20th century by efforts of many scientists including V. Ambartsumian,
S. Chandrasekhar, P. Debye, H. C. van de Hulst, G. Mie, and V. Sobolev, the light
scattering media optics still have many puzzles to be solved such as radiative
transfer in closely packed media, 3D radiative transfer as applied to the solution of
inverse problems, optics of terrestrial and planetary surfaces, etc. Also it has a broad
range of applications in many branches of modern science and technology such as
biomedical optics, atmospheric and oceanic optics, and astrophysics, to name a few.
It is planned that the Series will raise novel scientific questions, integrate data
analysis, and offer new insights in optics of light scattering media.
More information about this series at http://www.springer.com/series/15365
Alexander Kokhanovsky
Editor
Springer Series in Light
Scattering
Volume 1: Multiple Light Scattering,
Radiative Transfer and Remote Sensing
123
Editor
Alexander Kokhanovsky
Vitrociset Belgium
Darmstadt
Germany
ISSN 2509-2790 ISSN 2509-2804 (electronic)
Springer Series in Light Scattering
ISBN 978-3-319-70795-2 ISBN 978-3-319-70796-9 (eBook)
https://doi.org/10.1007/978-3-319-70796-9
Library of Congress Control Number: 2017957680
© Springer International Publishing AG 2018
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Contents
1 Invariant Imbedding Theory for the Vector Radiative
Transfer Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Curtis D. Mobley
2 Multiple Scattering of Light in Ordered Particulate Media . . . . . . . 101
Valery A. Loiko and Alexander A. Miskevich
3 Fast Stochastic Radiative Transfer Models for Trace Gas
and Cloud Property Retrievals Under Cloudy Conditions . . . . . . . . 231
Dmitry S. Efremenko, Adrian Doicu, Diego Loyola
and Thomas Trautmann
4 Neural Networks and Support Vector Machines and Their
Application to Aerosol and Cloud Remote Sensing: A Review . . . . . 279
Antonio Di Noia and Otto P. Hasekamp
5 Stereogrammetric Shapes of Mineral Dust Particles . . . . . . . . . . . . . 331
Olli Jokinen, Hannakaisa Lindqvist, Konrad Kandler,
Osku Kemppinen and Timo Nousiainen
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359
v
Contributors
Adrian Doicu Institut für Methodik der Fernerkundung (IMF), Deutsches
Zentrum für Luft- und Raumfahrt (DLR), Weßling, Oberpfaffenhofen, Germany
Dmitry S. Efremenko Institut für Methodik der Fernerkundung (IMF), Deutsches
Zentrum für Luft- und Raumfahrt (DLR), Weßling, Oberpfaffenhofen, Germany
Otto P. Hasekamp SRON Netherlands Institute for Space Research, Utrecht, The
Netherlands
Olli Jokinen Espoo, Finland
Konrad Kandler Institut fuer Angewandte Geowissenschaften, Technische
Universität Darmstadt, Darmstadt, Germany
Osku Kemppinen Finnish Meteorological Institute, Helsinki, Finland
Hannakaisa Lindqvist Finnish Meteorological Institute, Helsinki, Finland
Valery A. Loiko Institute of Physics, National Academy of Sciences of Belarus,
Minsk, Belarus
Diego Loyola Institut für Methodik der Fernerkundung (IMF), Deutsches Zentrum
für Luft- und Raumfahrt (DLR), Weßling, Oberpfaffenhofen, Germany
Alexander A. Miskevich Institute of Physics, National Academy of Sciences of
Belarus, Minsk, Belarus
Curtis D. Mobley Sequoia Scientific, Inc., Bellevue, WA, USA
Antonio Di Noia SRON Netherlands Institute for Space Research, Utrecht, The
Netherlands
Timo Nousiainen Finnish Meteorological Institute, Helsinki, Finland
Thomas Trautmann Institut für Methodik der Fernerkundung (IMF), Deutsches
Zentrum für Luft- und Raumfahrt (DLR), Weßling, Oberpfaffenhofen, Germany
vii
Abbreviations
1D, 2D, 3D One-dimensional, two-dimensional, three-dimensional
CPA Coherent potential approximation
DDA Discrete dipole approximation
EFA Effective field approximation
EM Electromagnetic
EMA Effective medium approximation
fcc Face-centered cubic
FDTD Finite difference time domain
FOV Field of view
IA Interference approximation
KKR Korringa–Kohn–Rostoker (method)
LC Liquid crystal
LEED Low-energy electron diffraction
LMS Layer-multiple-scattering (method)
PBG Photonic band gap
PC Planar crystal
PCF Pair correlation function
PDLC Polymer-dispersed liquid crystal
PhC Photonic crystal
QCA Quasicrystalline approximation
RDF Radial distribution function
RTE Radiative transfer equation
SC Solar cell
SNOM Scanning near-field optical microscopy
SPR Surface plasmon resonance
SSA Single scattering approximation
TIR Total internal reflection
TMM Transfer-matrix method
TMSW Theory of multiple scattering of waves
VSWF Vector spherical wave function
ix
Chapter 1
Invariant Imbedding Theory for the Vector
Radiative Transfer Equation
Curtis D. Mobley
1.1 Introduction
This chapter develops invariant imbedding theory as needed to solve the time-
independent vector (polarized) radiative transfer equation (VRTE) for a plane-
parallelwater body bounded by awind-blown sea surface and a reflective bottom. The
scalar (unpolarized) version of invariant imbedding theory applied to the same geom-
etry is described in Light and Water (Mobley 1994) and is employed in the widely
used HydroLight software (www.hydrolight.info). The development here parallels
that work and extends the scalar equations to the vector level. However, there are
additional complications in the vector theory because of loss of certain symmetries
in going from the scalar to the vector theory.
The radiative transfer problem for this geometry requires solution of a linear
integro-differential equation (the VRTE) subject to boundary conditions at the sea
surface and bottom, which may be either finitely or infinitely deep. The VRTE con-
stitutes a local formulation of the radiative transfer problem, which means that the
equation involves spatial derivatives of the relevant variables (the radiance in the
present case) and that the properties of the medium (the absorption and scattering
properties) are described by their values at each point in space (Preisendorfer 1965).
The essence of invariant imbedding theory as applied to transport problems is
that it transforms this local, linear, two-point boundary value problem to a pair of
non-linear initial values problems in the form of ordinary differential equations for
diffuse reflectances and transmittances (Preisendorfer 1958; Bellman et al. 1960).
The solution in terms of reflectances and transmittances is a global formulation of
the problem, which considers the response of the medium (e.g., the reflectance and
transmittance of finitely thick layers of water or even of the ocean as a whole) to its
inputs (e.g., the radiance incident onto the sea surface).
C. D. Mobley (B)
Sequoia Scientific, Inc., 2700 Richards Road, Suite 107, Bellevue, WA, USA
e-mail:
2 C. D. Mobley
The seminal idea of invariant imbedding theory in the geophysical setting traces
back to Ambartsumian (1943), who was interested in computing the reflectance
of light by planetary atmospheres. He realized that adding a layer of material to
an optically infinitely thick medium leaves the reflectance unchanged (invariant).
(Stokes (1862) used a similar idea to compute the reflectance of a stack of plates.)
From this idea, Ambartsumian was able to derive an equation that could be solved for
the reflectance of the entire atmospherewithout first having to compute the radiance at
each depthwithin the atmosphere. Thiswas a pioneering global solution of a radiative
transfer problem. Ambartsumian’s idea was further developed by many others, most
notably Chandrasekhar (1950), Sobolev (1956), Bellman and Kalaba (1956), and
Preisendorfer (1958). The formulation used here follows that of Preisendorfer as
presented for the scalar theory in his Hydrologic Optics treatise (Preisendorfer 1976).
The validity of radiative transfer theory rightly has been questioned
(e.g., Preisendorfer 1965; Mishchenko 2013a, 2014) because of its phenomeno-
logical nature and heuristic (and sometimes physically indefensible) assumptions
and derivations. R.W. Preisendorfer, a mathematician, worked to develop mathemat-
ically rigorous formulations of concepts such as radiance and invariance principles
(Preisendorfer 1965, 1976).More recently,M.I.Mishchenkohas expended enormous
effort over many years to develop a physically and mathematically rigorous connec-
tion between Maxwell’s equations and the VRTE, or as Preisendorfer (1965, p. 389)
worded it, to construct “an analytical bridge between the mainland of physics and the
island of radiative transfer theory.” That connection is now rigorous (Mishchenko
2008a, 2016). Fortunately, after all of the physical and mathematical dust has settled,
the VRTE still stands as a useful approximation to reality that gives results that are,
for a wide range of situations, sufficiently accurate for many problems (Mishchenko
2013b). The detail and rigor that are lost in circumventing Maxwell’s equations are
often repaid by computational efficiency. The present paper therefore begins with
a particular form of the VRTE and does not worry further about its foundations or
interpretation.
The initial section formulates the problem in terms of continuous variables for
depth, direction, and wavelength. The continuous variables are then discretized as
needed for numerical solution of the equations. Boundary conditions at the air-water
surface and ocean bottom are discussed in detail. Much of the material in these
sections is well-known but is repeated here both for completeness and to emphasize
certain points.
The subsequent sections comprise the core of the development: the formula-
tion of invariant imbedding theory to solve the VRTE within the water body. The
VRTE is first partitioned into separate sets of equations for upwelling and down-
welling radiance, which is a key step for the application of invariant imbedding
theory (Preisendorfer 1958; Bellman et al. 1960). These equations are then Fourier
decomposed in the azimuthal direction. This leads first to local interaction equations,
which govern how infinitesimally thin layers of water reflect and transmit light, and
then to global interaction equations, which govern how finitely thick layers of water
reflect and transmit light. Upward and downward sets of differential equations are
developed for the operators occurring in the global interaction equations. Given the